A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms
The power flow equations in DC microgrids are nonlinear due to the presence of constant power terminals. In this context, a rigorous demonstration of the convergence and uniqueness of the solution for Newton’s method is required. This problem is particularly important in islanded microgrids, where t...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2019
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8950
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8950
- Palabra clave:
- Convex optimization
DC microgrids
Gradient systems
Power flow analysis
Constraint theory
Convex optimization
Nonlinear equations
Gradient systems
Inequality constraint
Micro grid
Optimization approach
Optimization modeling
Potential function
Power flow analysis
Power flow equations
Electric load flow
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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| dc.title.none.fl_str_mv |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| title |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| spellingShingle |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms Convex optimization DC microgrids Gradient systems Power flow analysis Constraint theory Convex optimization Nonlinear equations Gradient systems Inequality constraint Micro grid Optimization approach Optimization modeling Potential function Power flow analysis Power flow equations Electric load flow |
| title_short |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| title_full |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| title_fullStr |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| title_full_unstemmed |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| title_sort |
A Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithms |
| dc.subject.keywords.none.fl_str_mv |
Convex optimization DC microgrids Gradient systems Power flow analysis Constraint theory Convex optimization Nonlinear equations Gradient systems Inequality constraint Micro grid Optimization approach Optimization modeling Potential function Power flow analysis Power flow equations Electric load flow |
| topic |
Convex optimization DC microgrids Gradient systems Power flow analysis Constraint theory Convex optimization Nonlinear equations Gradient systems Inequality constraint Micro grid Optimization approach Optimization modeling Potential function Power flow analysis Power flow equations Electric load flow |
| description |
The power flow equations in DC microgrids are nonlinear due to the presence of constant power terminals. In this context, a rigorous demonstration of the convergence and uniqueness of the solution for Newton’s method is required. This problem is particularly important in islanded microgrids, where the power flow method determines the equilibrium point, which in turn is used for other analyses such as stability, optimal operation, and reliability. In this paper, we present a new concept associated with power flow equations, namely the potential function of the power flow. This function allows transforming the power flow problem into an optimization model and uses convex analysis for determining its convergence and the uniqueness of the solution. Being a scalar function, the potential of the power flow can give valuable geometrical insights on the problem. In addition, the optimization approach can be used to solve the power flow problem considering inequality constraints. Simulation results demonstrate the applicability of this approach in practice. © 2019, Brazilian Society for Automatics--SBA. |
| publishDate |
2019 |
| dc.date.issued.none.fl_str_mv |
2019 |
| dc.date.accessioned.none.fl_str_mv |
2020-03-26T16:32:39Z |
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2020-03-26T16:32:39Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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Artículo |
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publishedVersion |
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Journal of Control, Automation and Electrical Systems; Vol. 30, Núm. 5; pp. 794-801 |
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21953880 |
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https://hdl.handle.net/20.500.12585/8950 |
| dc.identifier.doi.none.fl_str_mv |
10.1007/s40313-019-00489-4 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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36449223500 56919564100 |
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Journal of Control, Automation and Electrical Systems; Vol. 30, Núm. 5; pp. 794-801 21953880 10.1007/s40313-019-00489-4 Universidad Tecnológica de Bolívar Repositorio UTB 36449223500 56919564100 |
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https://hdl.handle.net/20.500.12585/8950 |
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eng |
| language |
eng |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/restrictedAccess |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ Atribución-NoComercial 4.0 Internacional http://purl.org/coar/access_right/c_16ec |
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Recurso electrónico |
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Springer New York LLC |
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Springer New York LLC |
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2020-03-26T16:32:39Z2020-03-26T16:32:39Z2019Journal of Control, Automation and Electrical Systems; Vol. 30, Núm. 5; pp. 794-80121953880https://hdl.handle.net/20.500.12585/895010.1007/s40313-019-00489-4Universidad Tecnológica de BolívarRepositorio UTB3644922350056919564100The power flow equations in DC microgrids are nonlinear due to the presence of constant power terminals. In this context, a rigorous demonstration of the convergence and uniqueness of the solution for Newton’s method is required. This problem is particularly important in islanded microgrids, where the power flow method determines the equilibrium point, which in turn is used for other analyses such as stability, optimal operation, and reliability. In this paper, we present a new concept associated with power flow equations, namely the potential function of the power flow. This function allows transforming the power flow problem into an optimization model and uses convex analysis for determining its convergence and the uniqueness of the solution. Being a scalar function, the potential of the power flow can give valuable geometrical insights on the problem. In addition, the optimization approach can be used to solve the power flow problem considering inequality constraints. Simulation results demonstrate the applicability of this approach in practice. © 2019, Brazilian Society for Automatics--SBA.Recurso electrónicoapplication/pdfengSpringer New York LLChttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068227575&doi=10.1007%2fs40313-019-00489-4&partnerID=40&md5=b842b319e00d806052713731f89fb1fcA Potential Function for the Power Flow in DC Microgrids: An Analysis of the Uniqueness and Existence of the Solution and Convergence of the Algorithmsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Convex optimizationDC microgridsGradient systemsPower flow analysisConstraint theoryConvex optimizationNonlinear equationsGradient systemsInequality constraintMicro gridOptimization approachOptimization modelingPotential functionPower flow analysisPower flow equationsElectric load flowGarcés, AlejandroMontoya O.-D.Abdali, A., Noroozian, R., Mazlumi, K., Simultaneous control and protection schemes for DC multi microgrids systems (2019) International Journal of Electrical Power & Energy Systems, 104, pp. 230-245Boyd, S., Vandenberghe, L., (2004) Convex optimization, , Cambridge University Press, New York, NYCai, H., Xiang, J., Wei, W., Chen, M.Z.Q., V-dp/dv droop control for PV sources in DC microgrids (2018) IEEE Transactions on Power Electronics, 33 (9), pp. 7708-7720Capitanescu, F., Critical review of recent advances and further developments needed in AC optimal power flow (2016) Electric Power Systems Research, 136, pp. 57-68Dastgeer, F., Gelani, H.E., Anees, H.M., Paracha, Z.J., Kalam, A., Analyses of efficiency/energy-savings of DC power distribution systems/microgrids: Past, present and future (2019) International Journal of Electrical Power & Energy Systems, 104, pp. 89-100De Persis, C., Weitenberg, E.R., Dörfler, F., A power consensus algorithm for DC microgrids (2018) Automatica, 89, pp. 364-375Elsayed, A.T., Mohamed, A.A., Mohammed, O.A., DC microgrids and distribution systems: An overview (2015) Electric Power Systems Research, 119, pp. 407-417Eriksson, R., Beerten, J., Ghandhari, M., Belmans, R., Optimizing DC voltage droop settings for AC/DC system interactions (2014) IEEE Transactions on Power Delivery, 29 (1), pp. 362-369Garces, A., Uniqueness of the power flow solutions in low voltage direct current grids (2017) Electric Power Systems Research, 151, pp. 149-153Garcés, A., On the convergence of Newton’s method in power flow studies for DC microgrids (2018) IEEE Transactions Power Systems, 33 (5), pp. 5770-5777Hamad, A.A., Azzouz, M.A., El-Saadany, E.F., Multiagent supervisory control for power management in DC microgrids (2016) IEEE Transactions on Smart Grid, 7 (2), pp. 1057-1068Hubbard, J.H., Hubbard, B.B., (1999) Vector calculus, linear algebra, and differential forms a unified approach, , Prentice Hall, Englewood CliffsKitson, J., Williamson, S., Harper, P., McMahon, C., Rosenberg, G., Tierney, M., Bell, K., Gautam, B., Modelling of an expandable, reconfigurable, renewable DC microgrid for off-grid communities (2018) Energy, 160, pp. 142-153Li, J., Liu, F., Wang, Z., Low, S., Mei, S., Optimal power flow in stand-alone DC microgrids (2018) IEEE Transactions Power Systems, , https://doi.org/10.1109/TPWRS.2018.2801280Loomis, L.H., Sternberg, S., (2014) Advanced calculus, , World Scientific, SingaporeLu, X., Sun, K., Guerrero, J.M., Vasquez, J.C., Huang, L., Wang, J., Stability enhancement based on virtual impedance for DC microgrids with constant power loads (2015) IEEE Transactions on Smart Grid, 6 (6), pp. 2770-2783Montoya, O.D., Numerical approximation of the maximum power consumption in DC-MGs with CPLs via an SDP model (2018) IEEE Transactions on Circuits Systems II Express Briefs, , https://doi.org/10.1109/TCSII.2018.2866447Montoya, O.D., Gil-González, W., Garces, A., Optimal power flow on DC microgrids: A quadratic convex approximation (2018) IEEE Transactions on Circuits Systems II Express Briefs, , https://doi.org/10.1109/TCSII.2018.2871432Montoya, O.D., Garrido, V.M., Gil-González, W., Grisales-Noreña, L., Power flow analysis in DC grids: Two alternative numerical methods (2019) IEEE Transactions on Circuits and Systems II: Express BriefsNesterov, Y., Nemirovskii, A., (1994) Interior point polynomial algorithms in convex programming, 10, 1. , 1, SIAM studies applied mathematics, PhiladelphiaPatterson, B., DC, come home: DC microgrids and the birth of the “Enernet (2012) IEEE Power Energy Magazine, 10 (6), pp. 60-69Roy, T.K., Mahmud, M.A., Oo, A.M.T., Haque, M.E., Muttaqi, K.M., Mendis, N., Nonlinear adaptive backstepping controller design for islanded DC microgrids (2018) IEEE Transactions on Industrial Applications, 54 (3), pp. 2857-2873Simpson-Porco, J.W., Dorfler, F., Bullo, F., On resistive networks of constant-power devices (2015) IEEE Transactions on Circuits Systems II Express Briefs, 62 (8), pp. 811-815Stewart, J., (2008) Multivariable Calculus, , BelmontStott, B., Jardim, J., Alsac, O., Dc power flow revisited (2009) IEEE Transactions on Power Systems, 24 (3), pp. 1290-1300Tah, A., Das, D., An enhanced droop control method for accurate load sharing and voltage improvement of isolated and interconnected DC microgrids (2016) IEEE Transactions on Sustainable Energy, 7 (3), pp. 1194-1204http://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/8950/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/8950oai:repositorio.utb.edu.co:20.500.12585/89502023-05-26 09:51:28.905Repositorio Institucional UTBrepositorioutb@utb.edu.co |